3x – 4y = 10 5x + 4y = 6

6
[8.3: SOLVING SYSTEMS BY ELIMINATION] 1 We have learned how to solve linear systems by graphing and substitution. Now we will learn how to solve the linear systems by using a method called . Example 1: Solve the linear system using elimination: 3x – 4y = 10 5x + 4y = 6 Do you have x over x, y over y and equal sign over equal sign? Yup! Continue on. The y’s are already opposites. Our work here is done. Add the two equations. Solve the resulting equation. Take the answer from and plug it into either of the original equations and solve for the other unknown variable. Write your solution as a coordinate point or as a pair of values. Step 1 • Make sure that all of the variables and the equal sign are "lined up." Step 2 •Decide which coefficients you want to cancel out. To cancel out, they must be opposites. You might have to multiple the equations first! Step 3 • Add the two equations and solve new equation. (One variable should cancel out!) Step 4 •Take your answer to Step 3 and substitute it into either of the orginal equations. Step 5 • Write your solution as a coordinate point or as a pair of values. Write your questions here!

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Page 1: 3x – 4y = 10 5x + 4y = 6

[8.3: SOLVING SYSTEMS BY ELIMINATION] 1 We  have  learned  how  to  solve  linear  systems  by  graphing  and  substitution.  Now  we  will  learn  how  to  solve  the  linear  systems  by  using  a  method  called  ψψψψψψψψψψψ.    

Example 1: Solve the linear system using elimination:

3x – 4y = 10 5x + 4y = 6

Do you have x over x, y over y and equal sign over equal sign? Yup! Continue on….

The y’s are already opposites. Our work here is done. Add the two equations. Solve the resulting equation. Take the answer from and plug it into either of the original

equations and solve for the other unknown variable. Write your solution as a coordinate point or as a pair of values.

Step 1 • Make sure that all of the variables and the equal sign are "lined up."

Step 2 • Decide which coefficients you want to cancel out. To cancel out, they must be opposites. You might have to multiple the equations first!

Step 3 • Add the two equations and solve new equation. (One variable should cancel out!)

Step 4 • Take your answer to Step 3 and substitute it into either of the orginal equations.

Step 5 • Write your solution as a coordinate point or as a pair of values.

Write your questions here!

Page 2: 3x – 4y = 10 5x + 4y = 6

2   8.3:  SOLVING  SYSTEMS  BY  ELIMINATION   More Examples: 2. 2x – y = 12 3. x + 2y = 4 -2x – 3y = -12 -6x + 2y = -10 4. 4x – 3y = 8 5. 9x + 2y = 39 2x – 2y = 0 6x + 13y = -9

Write your questions here!

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Page 3: 3x – 4y = 10 5x + 4y = 6

Worksheet by Kuta Software LLC

H Q Show all of your work!X Practice 8.3 Systems of Equations (Elimination)Solve each system by elimination.

1)

x

y

x

y2)

x

y

x

y

3)

x

y

x

y4)

x

y

x

y

5)

x

y

x

y6)

x

y

x

y

-1-

Page 4: 3x – 4y = 10 5x + 4y = 6

Worksheet by Kuta Software LLC

7)

x

y

x

y8)

x

y

x

y

9)

x

y

x

y10)

x

y

x

y

11) Is the point (0, 0) a solution of the systemof linear equations below?

2x + y = 2 4x - 2y = 2

12) Is the point (

, 7) a solution of the system

of linear equations below?

4x + y = 12 -4x + 3y = 16

-2-

Page 5: 3x – 4y = 10 5x + 4y = 6

[8.3: SOLVING SYSTEMS BY ELIMINATION] 5

1. Solve the following system of equations using elimination.

2. You have just enough coins to pay for a loaf of bread priced at $1.95. You know you have a total of12 coins, with only quarters and dimes. Let Q = the number of quarters and D = the number ofdimes. Complete:

_______ + _______ = 12 Representing the number of coins.

0.10_______ + 0.25______ = $1.95 Representing the value of the coins.

Now, solve the linear system using elimination. (Hint: Multiply the second equation by -10!)

3. The table shows the number of apples needed to make apple pies and applesauce sold at a farmstore. During a recent picking at the farm, 169 Granny Smith apples and 95 Red Delicious appleswere picked. Write and solve a system to determine how many apple pies and how many batchesof applesauce can be made if every apple is used. (Hint: read across each row to create your equations!)

Type of Apple # Needed for π (Pie)

# Needed for Sauce

Total

Granny Smith 5 4 169 Red Delicious 3 2 95

2x + 2y = 2 -8x + 4y = 16

Page 6: 3x – 4y = 10 5x + 4y = 6

3. The Algebros are visting Michigan State University when they stumble upon a Girl Scout selling cookies. Sully orders 3 boxes of Tagalongs and 4 boxes of Somoas for $26. Brust isn't statisfied with such a small order and yells "UPGRADE!!" He then upgrades the order to 5 boxes of Tagalongs and 6 Boxes of Somoas which costs $41.

a. Write a system of linear equations to model the situation. (Let x = cost of a box of Tagalongs and y = cost of a box of Somoas.)

b. Solve your system of equations above using elimination to find the cost of each type of cookie.